Proper transfer function: Difference between revisions

Revision as of 12:25, 17 June 2005

Revision as of 00:54, 26 June 2005

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In [[control theory]], a '''Properproper [[transfer function]]''' denotes a [[transfer function]] wherein which the [[Degreedegree (mathematics)|degree]] of the numerator does not exceed the degree of the denominator.

== Proper in control theory ==

'''Proper''' denotes a [[transfer function]] where the [[Degree (mathematics)|degree]] of the numerator does not exceed the degree of the denominator.

=== Example ===

The following transfer function is '''proper'''

:<math> \textbf{G}(s) = \frac{\textbf{N}(s)}{\textbf{D}(s)} = \frac{s^{4} + n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4}}{s^{4} + d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}</math>

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:<math> deg(\textbf{N}(s)) = 4 \nleq deg(\textbf{D}(s)) = 3 </math>.

=== Implications ===

A proper transfer function will never grow unbounded as the frequency approaces infinity.

:<math> |\textbf{G}(\infty)| < \infty </math>

== See also ==

[[Strictly proper]].

=== Related ===

[[Strictly proper]].